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PostgreSQL is "genuinely" opensource - as is any project under a recognised opensource license and that includes a host of RDBM'es

MySQL happens to the most popular one, and that one Google uses internally, so...

while Oracle owns it there are forks which may or may not supercede "MySQL" - similar to the OpenOffice vs LibreOffice - altho i don't suggest Oracle will donate MySQL to Apache like they did with OpenOffice

You mention Derby and there are a couple of other pure Java RDBMS namely Hypersonic SQL and H2 which is my personal pick e.g. for test database during development

I would hope that Google will later add support for PostgreSQL

most of the cloud offerings seem to start with MySQL (being the most popular) and then introduce PostgreSQL later